Exoplanet Statistics and the Search for Earth Twins

Minitab Blog Editor 02 October, 2014

Astronomy is cool! And, it’s gotten even more exciting with the search for exoplanets. You’ve probably heard about newly discovered exoplanets that are extremely different from Earth. These include hot Jupiters, super-cold iceballs, super-heated hellholes, very-low-density puffballs, and ultra-speedy planets that orbit their star in just hours. And then there is PSR J1719-1438 which has the mass of Jupiter, orbits a pulsar, and is probably one giant diamond!

In this post, I'll use statistics to look at the overall planetary output from the Milky Way’s planet-making process. Where does Earth fit in the overall distribution of planets? In light of the extreme exoplanets, is Earth actually the oddball?  I’ll also look into the search for an Earth twin, and highlight data that suggest exciting finds down the road.

Our Sample of Exoplanets

We have 1,826 confirmed exoplanets! That’s a very good sample size, but is this sample representative of all planets? To obtain a representative sample, you need to collect a random sample. It’s easy to point our instruments at random stars, but that doesn’t guarantee a representative sample. Equipment characteristics may make certain types of exoplanets easier to detect than others, thus biasing the sample.

Let’s look at the two methods that have been used to discover the most exoplanets to see how the sample might be biased. These are the radial-velocity and transit methods of planet discovery.

illustration of the radial velocity method for detecting exoplanetsThere’s nothing better than working with data yourself to truly understand it! These data are from the Planetary Habitability Laboratory’s exoplanet catalog, and I encourage you get the free trial version of our statistical software and explore the data yourself. .

Radial-velocity method

Astronomers who use the radial-velocity method look for the wobble that an orbiting exoplanet causes in its star. The bigger the wobble, the easier the exoplanet is to detect. Large exoplanets that are close to small stars cause the largest wobbles and are, therefore, easier to detect by this method. Hot Jupiters are easiest to detect with this method because of their large size and close proximity to the star.

Transit method

The transit, or photometry, method measures the decrease in brightness as an exoplanet passes in front of the parent star. The Kepler space telescope uses the transit method and it was specifically designed to be able to detect Earth-size planets. For this to work, the orbits of the exoplanets have to be perfectly aligned from the astronomers' vantage point.

illustration of the transit method of detecting exoplanetsKepler must observe at least three transits to flag a candidate exoplanet. The multiple transits help rule out other potential reasons for a light decrease but doesn’t prove it’s a planet. These candidates need to be confirmed via other methods, such as direct imaging. Unfortunately, Kepler was crippled by a failure after four years of data collection. Consequently, detecting exoplanets much more than one AU out from its star is not expected with the Kepler data.

Method comparison

The histograms below show the distribution in mass and distance by detection method for all confirmed exoplanets.

Mass of exoplanet grouped by detection method

Exoplanet distance from parent star by detection method

Both methods found a large proportion of planets that are both close to the star and not particularly massive. Even the radial-velocity method, which favors massive planets, found more smaller planets. As expected, the Kepler stopped finding planets that are further than one astronomical unit (AU) away from their star, but the detections by radial-velocity continue out to greater distances.

So, while we probably don’t have a completely representative sample, the two methods agree on the general shape of the distribution: smaller, closer planets far out number massive, more distant planets.

Overall Distribution of Exoplanets

Next, we’ll look at the overall distribution of all confirmed exoplanets by several key variables. The green bar in each graph shows where the Earth fits in.

Histogram of mass of confirmed exoplanets

We can see that the range in exoplanet mass varies greatly, from very small to thousands of Earth masses. For comparison, Jupiter is 317 Earth masses. There are many more small planets, like Earth, than large planets! Let's zoom in.

Zoomed in look at mass of Earth-sized planets

In this graph, I've truncated the X-axis. Here we can see that Earth is actually smaller than the peak value. Among rocky planets, it turns out that super-Earths are more common than Earth-sized planets. Super-Earths are rocky like Earth, but have 2 to 5 times the mass of Earth. So, Earth might be slightly unusual for rocky planets by being on the small side.  

Average distance of exoplanet from parent star

Earth is a bit further from the sun (1 AU) than the more frequent distances on the graph. This reflects the fact that red dwarf stars are by far the most common type of star (80%). These smaller, cooler stars have planetary systems that are much more compact than those of stars like our sun.

Orbital eccentricity of confirmed exoplantes

Orbital eccentricity measures whether an object's orbit is close to circular or more elliptical (oval shaped). Highly eccentric orbits cause extreme climate changes because there is a greater difference between the minimum and maximum distances from the parent star.

Zero is a perfect circle while just less than one is the most elliptical an orbit can be. The orbits of the planets in the solar system are very circular. We can see on the graph that Earth's very low eccentricity is not unusual among confirmed exoplanets.

These graphs show that Earth really isn’t such an oddball—there’s a wide range of planets, and Earth falls near the more common values in each graph.

The Search for an Earth Twin

There’s more to our search than just looking at the distributions by mass, length of year, and orbital eccentricity. We want to know about specific cases where everything lines up just right to produce exoplanets that are habitable Earth twins.

Let me introduce you to the Earth similarity index (ESI). This measure indicates how similar an exoplanet is to Earth. Values range from 0 to 1, where Earth has a value of one. ESI is based on estimated parameters for each exoplanet, such as radius, density, surface temperature, and escape velocity. In our solar system, Mars has an ESI of 0.64 and Venus is 0.78.

The bubbleplot below shows all of the confirmed exoplanets and unconfirmed Kepler candidates that have ESI values greater than 0.80 and are in the habitable zone. For comparison, the blue bubble is Earth.

Bubbleplot of Earth-like exoplanets by mass, length of year, and star mass

There are 23 exoplanets and candidates that have an ESI greater than 0.80. In fact, five are greater than or equal to 0.90, with the highest being 0.93. The blue Earth bubble is smaller than most other bubbles on the plot, which again indicates that Earth is on the smaller side for rocky planets. On the graph, 18 out of 23 (78%) are super-Earths, four are classified as Earth-sized, and one is smaller than Earth.

Even though a majority are super-Earths, that’s fine because, super-Earths might be even more habitable than Earth-sized planets!

There are two groups of Earth-like planets on the graph. Let’s call them Earth cousins and Earth twins.

The Earth cousins are on the bottom-left. These exoplanets are similar to Earth, but they orbit red dwarf stars that are much cooler and less massive than our sun. These exoplanets need to orbit much closer to be in the habitable zone, which produces the short years.

The Earth twins are on the top right. These exoplanets are like Earth and orbit stars that are like our sun. Consequently, they have years that are more similar to our own.

The bubbleplot contains both confirmed planets and unconfirmed Kepler candidates. The green bubbles indicate confirmed planets, but they’re all in the Earth cousin group. So far, all Earth twins are unconfirmed by other methods. Kepler has detected three transits for each candidate, but some of the candidates may be false positives. The false positive rate for Kepler candidates varies by planet size, and for Earth-sized planets it is 12.3%.

While it is reasonable to expect that some of the 14 Earth twins are false positives, we can also expect that 88% (12) will eventually be confirmed. That will be exciting news! And those are just the twins that we currently have data for.

Given the context about the distribution of planets, it’s not surprising that scientists estimate there are 40 billion Earth-sized planets in the habitable zones of their stars in the Milky Way!

The image of the radial velocity method is by Rnt20 and the image of the planet transit method is by Nikola Smolenski. Both images are used under this Creative Commons license.